Thanks a lot for the responses. Ok, so it is called a headliner.... how did I miss that? :-)
So, the consensus is that no one has succeeded gluing it back on because of the deteriorated foam on the fabric. 180's temp solution definitely is temporary... I thought about using a clear sealant used for roof repair. It goes on like a gel so it will have the bulk (unlike a glue spray) and it has the power to hold things but I just don't know what it will be like longer term. For those of you who have resorted to an upholsterer, did he/she replace the headliner or reused it?